Versatility of the dipolar filter selection: from 1H nuclear spin diffusion experiment to the measurement of nuclear Overhauser effect in homopolymer melts

Dipolar filters select ¹H magnetization according to local dipolar dephasing, which corresponds to site mobility in systems with heterogeneous molecular mobility. Combined with a conventional exchange experiment, it is usually applied to polymeric samples exhibiting structures on the nanometer length scale associated with a strong dynamic contrast. There, the resulting ¹H nuclear spin diffusion experiment yields the size of the structure. When the same experiment is applied to homopolymer melts exhibiting a weak dynamic contrast and dynamic heterogeneities on significant shorter length scales, the recorded magnetization decay is in agreement with decays expected from a heterogeneous nanostructure. However, dipolar filters actually can also select mobile parts of the repeat unit, e.g. the end of the alkyl side chains and the subsequent magnetization transfer then can occur via cross relaxation due to non coherent zero-quantum transitions (nuclear Overhauser effect, NOE). The difficulties of distinguishing these two cases are examined and it is demonstrated that NOE experiments exploiting magnetization selection via the dipolar filter allow quantifying the local dynamics of the side chains. This opens new possibilities for measurements of local dynamics in non isotopically labeled homopolymer melts.     

Effects of zero-filling and apodization on spectral integrals in discrete Fourier-transform spectroscopy of noisy data

The influence of noise on the standard deviation of spectral integrals is examined. Calculations assuming discrete Fourier-transform data are compared with Monte-Carlo simulations. The effects of zero-filling and apodization are examined for free-induction-decay (FID) signals and for symmetric spin-echo signals in one and two dimensions, with particular attention to features not previously presented in the literature. Findings suggest that for mild apodization, the known sensitivity enhancement due to zero-filling in either the real or the imaginary part signal [E. Bartholdi, R.R. Ernst, Fourier spectroscopy and the causality principle, J. Magn. Reson., 11 (1973) 9-19] is maintained; however, for stronger apodization filters, this enhancement can be obliterated completely. It is shown that results obtained by analysis of one-dimensional signals can be readily applied to multi-dimensional data. Furthermore, zero-filling has a negligible effect for symmetric spin-echo signals with implications for signal averaging in magnetic resonance imaging and spectroscopic imaging.     

Electro-optic properties of nematic and ferroelectric liquid crystalline nanocolloids doped with partially reduced graphene oxide

Flakes of partially reduced graphene oxide (PRGO) were doped in nematic liquid crystals (NLCs) and ferroelectric liquid crystals (FLCs), respectively. The dielectric and electro-optical properties of NLCs doped with those flakes have been investigated. Threshold voltage and switching times are reduced by 30%–50%. This is primarily due to the decrease of the elastic properties of the nanocolloids compared to the non-doped nematics. The influence of the PRGO flakes on the spontaneous polarization, tilt angle and switching time of FLCs was investigated too. Such flakes reduce the response time by 40%–60%, increases spontaneous polarization by 20%–25% and increase the tilt angle by 15%–20%.     

Universal resources for measurement-based quantum computation

We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess the universality of graph states by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal nongraph state.     

Quadruplex CARS micro‐spectroscopy

We demonstrate a technique for simultaneous detection of coherent anti‐Stokes Raman scattering (CARS) at four vibrational frequencies, using simple passive optical elements and without spectrally resolved detection. The technique is based on pump and Stokes femtosecond pulses selectively exciting vibrational resonances through spectral focusing. By replicating the pump and Stokes pair into four pairs, each traveling through appropriate glass elements, we simultaneously excite four different vibrational frequencies. The resulting CARS is a periodic train of intensities detected by a single photomultiplier and frequency analyzed to retrieve its Fourier coefficients. We demonstrate detection of methanol and ethanol mixtures in water and quantitative determination of their concentration owing to the improved chemical selectivity of this quadruplex CARS scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Interaction-induced collapse of a section of the Fermi sea in the zigzag Hubbard ladder

Using the next-nearest-neighbor (zigzag) Hubbard chain as a one-dimensional model, we investigate the influence of interactions on the position of the Fermi wave vectors with the density-matrix renormalization-group technique. For suitable choices of the hopping parameters we observe that electron-electron correlations induce very different renormalizations for the two different Fermi wave vectors, which ultimately lead to a complete destruction of one section of the Fermi sea in a quantum critical point.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.     

Vector fields on complex quantum groups

Using previous results we construct theq-analogues of the left invariant vector fields of the quantum enveloping algebra corresponding to the complex Lie algebras of typeA _n–1 ,B _n ,C _n , andD _n . These quantum vector fields are functionals over the complex quantum groupA. In the special caseA ₁ it is shown that this Hopf algebra coincides withU _q sl(2, ).